I neglected to mention that, once you get either I_theta or some empirical estimate of it, you then invert it to get an estimate of the asymptotic covariance matrix of the MLE.
On Tue, Jan 22, 2013 at 3:48 PM, Mark Leeds <marklee...@gmail.com> wrote: > Hi Doug: I was just looking at this coincidentally. When X is a vector, > the Fisher Information I_{theta} = the negative expectation of the second > derivatives of the log likelihood. So it's a matrix. In other words, > I_theta = E(partial^2 /partial theta^2(log(X,theta).) where X is a vector. > > But, even though the the Fisher Information has a seemingly nice formula, > ( and this is where my confusion arose when I was dealing with this and why > I'm looking at it right > now. I have short document that I wrote to myself explaining it so if > anyone wants it, email me individually. It's nothing earth shattering !!!!! > ) in many cases taking the that expectation is not easy so the Fischer > Information is approximated by its empirical counterpart which is obtained > by summing each of the elements in the matrix given the n observations and > then dividing each of the elements in the matrix by n. > > > > > > > > > > > > > > On Tue, Jan 22, 2013 at 3:27 PM, Douglas Bates <ba...@stat.wisc.edu>wrote: > >> Your question is better addressed to the R-help@R-project.org mailing >> list, >> which I am copying on this reply. >> >> You are confusing a statistical concept, the Fisher Information matrix, >> with a numerical concept, the Hessian matrix of a scalar function of a >> vector argument. >> >> The Fisher information matrix is the Hessian matrix of a particular >> function at its optimum and I have forgotten whether that function is the >> log-likelihood or negative twice the log-likelihood or ... Rather than >> get >> it wrong I am sending a copy of this reply to the list where many of the >> readers will be able to answer you more reliably than I can. >> >> >> On Tue, Jan 22, 2013 at 1:22 PM, Marcos Coque Jr <mcoqu...@yahoo.com.br >> >wrote: >> >> > Dear Bates, >> > >> > I am using the fdHess function for R language. >> > And I have a question. >> > >> > What is the relationship with the Hessian and Fisher Information in your >> > function? >> > Because I think that Fisher Information=-Hessian, but I found the >> oposite >> > in your function. >> > Maybe I be something wrong... >> > >> > Thanks, >> > >> > Marcos >> > >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> > > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.